The theory of determinants in the historical order of development, by Sir Thomas Muir.

LESS COMMON SPECIAL FORMS (CAYLEY, 1845) 461
but that for higher orders the result is 0. He next notes the
identity
X X 95 X
X' X ' X X X
adding "etc. for determinants of any order";* and then from
this set of identities and the previous set he concludes that if
any four adjacent columns of a quaternion determinant be
transposed in every possible manner, the sum of the determinants thus obtained vanishes-a property which, he says, is
much less simple than the analogous one for the rows, this last
being the same that holds in the case of determinants with
ordinary elements. Lastly, he gives the important warning that
the eliminant of
'rI + 05 = 0
7r'H + ' = O
is neither rq'-vr'q nor 7rqS'- sr', but
-_, _,- 1,/
TISSOT, A. (1852, May).
[Sur un determinant d'integrales definies. Journ. (de Liouville)
de Math., xvii. pp. 177-185.]
The subject here is the evaluation of the determinant of the
(n+ i)th order whose (r, s)th element is,as - x rc d x
%-i
* Very probably the next case is the identity
0 X% 0 b X X 0 X 0
0' X' X ' + X' X' x' + X/ X ' +...+ g,' x' o'
c,, x, t //,,/, ~ x" x,", 0', A" / x" Of"
q5 q50 F q5 0 0 ' ~ ',~,' I 0" 0" q5"
= X X XX X X" X" - X X X +..- x' X' X'
/f/" q" y / ^ / // q" V" W 1P X
where, as in the other cases, the rth determinant on the left is equal to the
aggregate of the rth terms of all the determinants on the right.